What is the Greatest Common Factor of 29760 and 29770?

Greatest common factor (GCF) of 29760 and 29770 is 10.

GCF(29760,29770) = 10

We will now calculate the prime factors of 29760 and 29770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29760 and 29770.

How to find the GCF of 29760 and 29770?

We will first find the prime factorization of 29760 and 29770. After we will calculate the factors of 29760 and 29770 and find the biggest common factor number .

Step-1: Prime Factorization of 29760

Prime factors of 29760 are 2, 3, 5, 31. Prime factorization of 29760 in exponential form is:

29760 = 2⁶ × 3¹ × 5¹ × 31¹

Step-2: Prime Factorization of 29770

Prime factors of 29770 are 2, 5, 13, 229. Prime factorization of 29770 in exponential form is:

29770 = 2¹ × 5¹ × 13¹ × 229¹

Step-3: Factors of 29760

List of positive integer factors of 29760 that divides 29760 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 32, 40, 48, 60, 62, 64, 80, 93, 96, 120, 124, 155, 160, 186, 192, 240, 248, 310, 320, 372, 465, 480, 496, 620, 744, 930, 960, 992, 1240, 1488, 1860, 1984, 2480, 2976, 3720, 4960, 5952, 7440, 9920, 14880

Step-4: Factors of 29770

List of positive integer factors of 29770 that divides 29760 without a remainder.

1, 2, 5, 10, 13, 26, 65, 130, 229, 458, 1145, 2290, 2977, 5954, 14885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29760 and 29770. The biggest common factor number is the GCF number.
So the greatest common factor 29760 and 29770 is 10.

Also check out the Least Common Multiple of 29760 and 29770